What is the general solution for cos(4x)=sin(2x) ?

The general solution for cos(4x)=sin(2x) is x=(3pi)/4+pin,x= pi/(12)+pin,x=(5pi)/(12)+pin

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cos(4x)=sin(2x)

cos (4 x) = sin (2 x)

x = \frac{3 π}{4} + πn, x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Solution steps

cos (4 x) = sin (2 x)

Subtract

sin (2 x)

from both sides

cos (4 x) - sin (2 x) = 0

Rewrite using trig identities

1 - sin (2 x) - 2 sin^{2} (2 x) = 0

Solve by substitution

sin (2 x) = - 1, sin (2 x) = \frac{1}{2}

sin (2 x) = - 1 : x = \frac{3 π}{4} + πn

sin (2 x) = \frac{1}{2} : x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

csc (θ) = 2

- sin (x) - cos (x) = 0

sec (x) sin (x) - 2 sin (x) = 0

4 cos^{2} (x) = 3

cos (3 x) = - \frac{1}{2}

What is the general solution for cos(4x)=sin(2x) ?
The general solution for cos(4x)=sin(2x) is x=(3pi)/4+pin,x= pi/(12)+pin,x=(5pi)/(12)+pin